f is functional. MRIs are basically huge magnets used for imaging. When you apply a strong magnetic field, different tissue types and densities will react differently, and the MRI is basically measuring how those tissues react to the magnet. It is very good for imaging soft tissues, but not so much bone. Someone figured out that you can measure blood flow using the MRI, because blood cells react in a magnetic field, then "relax" at a known rate. Since we can measure blood flow, that is correlated with increased brain activity, i.e. since more neurons are firing, they require more energy, and therefore more blood. So, fMRI is using blood flow as a proxy for brain activity.